General respect level: physics or math?

[galoiauss]

Just wondering, what is the general consensus on whether physics or math is a more respectable and "harder" intellectual field. I'm a mathematician, and I know both can be very hard, but just wanted to know on a simple level. I'm asking this in the same light as how people usually rank the sciences in terms of their difficulty/pureness/respect level (eg. bio< chem < ...)

 

[radou]

There is a joke which says: 'Chemists think they're physicians; physicians think they're mathematicians; mathematicians think they're gods.'

Joke aside, I don't think one can draw conclusions about that in general. Of course, for example, knowing a lot math makes it easier for one to learn some physics, but that means nothing.

 

[matt grime]

A physician is a doctor, as in medical doctor. I think you might have meant physicist.

 

[radou]

A physician is a doctor, as in medical doctor. I think you might have meant physicist.

Yes, I meant physicist, thanks.

 

[MeJennifer]

There is a joke which says: 'Chemists think they're physicians; ...

Well considering the focus of western medicine to fix everything will a pill..

 

[pivoxa15]

From my undergradate experiences, I'd consider the levels of difficulty from most to least: experimental physics<pure maths<theoretical physics<applied maths

I put experimental physics at the top due to my lack of experience with experimental science and low level of kowledge of general physics (i.e. how things work) and the huge amount of vaguenss that occurs in undergrad lab classes which really puts me off.

From observing other students I have noticed that good at maths => good at physics but not always the other way around. I feel that physics always takes small sections of maths and combine many applications with it. So in this way physics is a branch of maths and so maths is more general. General things are considered harder than special things, in general. As Dyson said, Mathematicans are like birds flying across the field whereas physicists are like frogs leaping around in the same field but being able to see it more closely but obviously not as far.

From observation from academics in both departments I conclude that mathematicians are 'smarter' than physicists. Although the word smart is subjective. Maybe its the fact that mathematics is precise which makes the arguments made by mathematicans to be more solid or less hand waving. And nothing beats elegant maths proofs because not only is it 100% correct, its also delivered in an efficient manner. Just reading these things can make one smarter.

The more maths a physicist uses, the smarter they seem. i.e Witten. And people like Witten are considered the best physicists. A mathematician knowing more physics doesn't neccessiarly make them better mathematicians but a physicst who knows more maths will definitely make them better physicists so in this way (and the other reasons given), maths is more respectable.

Although having said all this here is a thread that might give some different views.

https://www.physicsforums.com/showthread.php?t=80027

 

[CRGreathouse]

I think that by asking this in a math forum you're going to get a lot of responses biased in that direction.

For my part, I tend to agree with pivoxa15 -- and have had the same experience with math professors vs. other professors in terms of general intelligence. Of course its all very subjective.

 

[Alkatran]

The question you're actually asking here is "Is math/physics preference correlated with IQ?" If they aren't correlated, then we expect people of the same intelligence to go in both fields and cover all the 'low hanging fruit' at their level.

There should be some sort of study done.


... Yes, I know IQ is a bad measure of intelligence.

 

[pivoxa15]

You could also look at this problem from the perspective of which field of study can be learned by self study most easily.

At first one thinks that maths can more easily learned than (theoretical) physics because it is purely a priori. But from experience it is not the case because a priori doesn't mean it is easier to learn. It takes a lot of training and effort to see these a priori truths. With physics, one has an intuitive feel more so than maths and plus the hardest things in physics are usually the maths. In this way, maths is harder to self learn than physics.

 

[radou]

The question you're actually asking here is "Is math/physics preference correlated with IQ?" If they aren't correlated, then we expect people of the same intelligence to go in both fields and cover all the 'low hanging fruit' at their level.

There should be some sort of study done.


... Yes, I know IQ is a bad measure of intelligence.

Btw, in my opinion, IQ (measured as it is) is a factor related only to the speed and time of study, mostly, under assumption that the person is average (or slightly below).

 

[mathwonk]

i think math must be the easiest of all fields, as it is the only one i could ever understand anything in.

 

[Gib Z]

Lol hilarious mathwonk. Personally, I think mathematicians are the most respectable, at least between them and physicists. Physicists are smart, but not as much so as mathematicians. Albert Einstein piggybacked on Riemann with General Relativity, but not as many people know who Riemann is. Mathematicians will be able to do a physicists job for a day and won't be too bad, maybe even better. A physicist will cry at a mathematicians, unless its a string theorist, then they may fair alright. I like to think of physics as applied math, which makes me think math is more pure. Math is the language of physics.

Another example, Gauss was an excellent mathematician, and did physics as a hobby and still made contributions the average physics student would be dreaming to achieve.

 

[pivoxa15]

Fair point Gib Z. Theoretical physicists are just like applied mathematicians although less rigorous.

How many physicists who started out as pure mathematicians? A few.
How many pure mathematicians started out as physicists? I can't think of any.

 

[pivoxa15]

i think math must be the easiest of all fields, as it is the only one i could ever understand anything in.

I can see how this impression comes about. I think it is hard to learn maths but once you have learned it, you think how easy it is because it should be self evident truths. Whereas with the other subjects, most deal with empirical objects that are naturally not well defined so the concepts may be easier and learning it for the first time may be quicker and easier than maths but one can never 'understand' those empirical subjects - at least not in the way one could 'understand' mathematics.

 

[Werg22]

Nothing prevents a physicist from being a very strong mathematician. The opposite is also true.

 

[andytoh]

To specialize in, say, superstring theory, you have to learn mountains of mathematics, as well as know all the basic physics topics as well as the difficult specialized topics like relativity and quantum field theory. But a mathematician does not need to learn any physics at all. A mathematical physicist is capable of earning two different PhDs, one in math and one in physics. On the other hand, a pure mathematician cannot earn a PhD in physics and a pure physicist cannot earn a PhD in mathematics (unless and take the time to study the other subject from scratch). This is why I admire mathematical physicists like Hawking and Penrose.

 

[pivoxa15]

To specialize in, say, superstring theory, you have to learn mountains of mathematics, as well as know all the basic physics topics as well as the difficult specialized topics like relativity and quantum field theory. But a mathematician does not need to learn any physics at all. A mathematical physicist is capable of earning two different PhDs, one in math and one in physics. On the other hand, a pure mathematician cannot earn a PhD in physics and a pure physicist cannot earn a PhD in mathematics (unless and take the time to study the other subject from scratch). This is why I admire mathematical physicists like Hawking and Penrose.

At my university, you could potentially do a Phd in mathematical physics without having done any undergraduate physics. So when these people (who haven't done any undergrad physics) become mathematical physicists in the maths department , I am not sure they can study a second Phd in the physics department straight away?

 

[matt grime]

A mathematical physicist is capable of earning two different PhDs, one in math and one in physics.

I'm not sure you'll find that is true. At least no more true than the next quote:

On the other hand, a pure mathematician cannot earn a PhD in physics and a pure physicist cannot earn a PhD in mathematics (unless and take the time to study the other subject from scratch).

is true. Not least because your favoured area of string theory is very likely to be studied by a pure mathematician. In fact I know very few applied people, or those with a physical background who do string theory, and many pure mathematicians.

I would also like to point out that plenty of pure mathematicians have a more than average working knowledge of relativity and quantum mechanics - they are after all undergraduate course. I even know some people who did these subjects for personal interest during Part III and are very pure mathematicians. Just as there are plenty of applied people who have a working knowledge of representation theory, say. The pure mathematics of string theory (that wouldn't be assumed from, say, relativity) and are essectial to the beginner can be summed up as:

essential: Riemann surfaces
useful: category theory, algebraic topology/geometry

all but category theory can be, and is, learned to reasonable level as an undergraduate course. Category theory might be taught, but is often overlooked. To be honest, outside of Baez's n-categorical viewpoint, I'm not sure how useful this really is. The student may end up knowing some highly specialized stuff (in some sense) like chern classes, and poincare duality, or McKay correspondence but it is by no means assured. At the last conference I attended dealing with such matters I don't think I saw a PhD student there, and only a handful of people on post-docs like me. And, no, I'm not a mathematical physicist.

I think it very misleading to imply that a recently qualified Maths Phys PhD is somehow a demigod of both subjects, and knows enough to do research in either. They don't. They certainly ought to know enough to do research in Maths Phys, but that is the only thing nearing a certainty you can say. You start learning the real stuff after the PhD, apparently. If I were you, I'd check out some PhD theses from maths phys students before saying what it is they have to know, and what it is they do at this stage.

This is why I admire mathematical physicists like Hawking and Penrose.

They are certainly admirable names. But an average mathematical physicist is no more or less able than an average mathematician/physicist. They just happen to work at a very fluid boundary.

 

[mathwonk]

i think it depends who you ask. i.e. in some circles mathematicians are regarded as hopeless knuckle draggers, and physicists the height of sophisticted intellectuals.

e.g this position is often heard forwarded in meetings of the flat Earth society, or of the kansas school board.

 

[Gib Z]

Thats exactly what I used to believe, only because I was a physicist :D matt grime may remember me from scienceforums.net, where I spent the majority of my time posting in the physics sections, and I thought i was good :p Then in my studies I realized to continue further in my physics I need a better understand of Calculus, which is when I started to become more interested in pure mathematics. Never Turned back :D I still don't know much in either field though, from what I know about the way American Studies are catergorized, I am up to Calc 3, not very good.

 

[Crosson]

The mathematical style is the pinnacle of orginazition and learning efficacy. A mathematician can quickly learn another field in its entirety if it is presented properly.

I vote that mathematicians receive more respect.

 

[mathwonk]

ill buy that!

 

[Azael]

Mathematicians will be able to do a physicists job for a day and won't be too bad, maybe even better.

Well let's do a experiment. Drag out a mathematician to cern and tell him to plan and run a experiment there.

 

[1016]

There is a joke which says: 'Chemists think they're physicians; physicians think they're mathematicians; mathematicians think they're gods.'

haha, I prefer this joke answer. That's why, i do like becomes these three specialist as well.

 

[Gib Z]

Well to tell you the truth, Several People is these forums could do that, I'm sure a good mathematician knows just as much physics as them. In fact, I know someone, he teaches at the University of New South Wales, in the mathematics department and the physics department pretty much works off him :P And anyway Azael, I was referring to the distinctions between applied mathematics and theoretical physics. Many will agree they somewhat address the same issues. One argument could be that theoretical physics is seen as somewhat more Pure than say, experimental. And pure math is more pure than applied. If the purest physics corresponds to less than the purest math, One may come to the conclusion math is a more pure and respectable field.

About the job analogy, let's say it like this. If I had 2 equally challenging problems, one Purely mathematical, and one in the Purest of Physics, and My life depended on me solving both, sure as hell id hope i was a mathematician :P

 

[mathwonk]

In my math department there is a seminar in physics, and there is an algebraic geometer by training who is a main participant. Physicists have been coming to him for consulation for years, and he has collaborated with them as well. Currently he has begun putting his primary research time into the questions arising in the physics seminar. So at least a few of the most gifted people in mathematics can seamlesly transition to mathematical physics.

Indeed some of my research on vector bundles on abelian varieties, and on their theta divisors could almost be rewritten and published as mathematical physics, simply by changing the terminology to invlove words like "Higgs fields" instead of certain line bundles. I know this because I have been an invited lecturer on related topics at the ICTP in Trieste, along with people like Nigel Hitchin.

 

[Azael]

Well to tell you the truth, Several People is these forums could do that, I'm sure a good mathematician knows just as much physics as them. In fact, I know someone, he teaches at the University of New South Wales, in the mathematics department and the physics department pretty much works off him :P And anyway Azael, I was referring to the distinctions between applied mathematics and theoretical physics. Many will agree they somewhat address the same issues. One argument could be that theoretical physics is seen as somewhat more Pure than say, experimental. And pure math is more pure than applied. If the purest physics corresponds to less than the purest math, One may come to the conclusion math is a more pure and respectable field.

About the job analogy, let's say it like this. If I had 2 equally challenging problems, one Purely mathematical, and one in the Purest of Physics, and My life depended on me solving both, sure as hell id hope i was a mathematician :P

I do not quite understand why you think a good mathematician knows as much physics as a good physicsist. If that was true physics educations would be useless and would be replaced by math educations. The mathematics professors I have had so far has not been physics gurus.

I don't have any stats to back this up, but I suspect most physicsist are experimentalists, there is no reason to believe a mathematician would be able to do a experimentalist job, hell most theoretical physicsists probably wouldn't be able to do a experimentalists job.
Remember that there are whole TEAMS of physicsists working on almost each important component of the big experiments like ATLAS.
It takes years of specialisation to do anything worthwhile and to claim a mathematician could just walk in there and replace a physicsist that has spent years working on something is ridicilous.

The small fragment of physicsists that work on string theory and similar things are really not a example of what the majority of physicsists do.

To argue what is most pure seems like just a way for people to stroke there own ego. IMO all fields of science are more or less equaly respectable.

 

[matt grime]

I do not quite understand why you think a good mathematician knows as much physics as a good physicsist.

Please post an example where people here have said that any mathematician knows as much physics as a physicist.

I don't have any stats to back this up, but I suspect most physicsist are experimentalists, there is no reason to believe a mathematician would be able to do a experimentalist job, hell most theoretical physicsists probably wouldn't be able to do a experimentalists job.

again, point out where anyone has said that they would be able to walk in and take over.

to claim a mathematician could just walk in there and replace a physicsist that has spent years working on something is ridicilous.

have a guess what I'm about to ask...About the *strongest* conclusion (reading between the lines, paraphrasing a little) I would say anyone has made here is that someone who has proved themselves capable of holding down a research position in mathematics is probably sufficiently talented to have held down a research position in any other subject if they had chosen that path, and that the converse is probably not true.

 

[mathwonk]

i suspect the respect i get purely because i am a mathematician, only lasts roughly until i open my mouth anyway.

 

[Gib Z]

Lol I reckon mathwonk would have won the Funniest Member prize if he didnt win the math won :p btw Azael, I never actually said a mathematician would be able to take over a physicists perfectly, just better so than a physicist could take over a mathematicians, pretty much what matt grime said.

Lets just all agree that, mathematicians and/or physicists represent the highest level of intellectualism, rather than say, chemists or one who professes in literature?